@Article{Kukelova-Pajdla-PAMI-2011,
  IS = { zkontrolovano 10 Jan 2012 },
  UPDATE  = { 2011-12-29 },
  author =       {Kukelova, Zuzana and
                  Pajdla, Tom{\' a}{\v s}},
  title =        {A Minimal Solution to Radial Distortion Autocalibration},
  journal =      {{IEEE} Transactions on Pattern Analysis and Machine Intelligence},
  volume =       {33},
  number =       {12},
  year =         {2011},
  month =        {December},
  publisher =    {IEEE Computer Society},
  address =      {Los Alamitos, USA},
  issn =         {0162-8828},
  pages =        {2410-2422},
  authorship =   {50-50},
  project =      {FP7-SPACE-241523 PRoViScout, MSM6840770038},
  keywords =     {minimal problems, radial distortion, 
    Gr{\" o}bner bases, polynomial eigenvalue problems},
  psurl = {http://dx.doi.org/10.1109/TPAMI.2011.86},
  annote = {Simultaneous estimation of radial distortion, epipolar
    geometry and relative camera pose can be formulated as a minimal
    problem and solved from a minimal number of image points. Finding
    the solution to this problem leads to solving a system of
    algebraic equations. In this paper we provide two different
    solutions to the problem of estimating radial distortion and
    epipolar geometry from eight point correspondences in two
    images. Unlike previous algorithms, which were able to solve the
    problem from nine correspondences only, we enforce the determinant
    of the fundamental matrix be zero. This leads to a system of eight
    quadratic and one cubic equations in nine variables. We first
    simplify this system by eliminating six of these variables and
    then solve the system by two alternative techniques. The first one
    is based on the Gr\"{o}bner basis method and the second one on the
    polynomial eigenvalue computation. We demonstrate that our
    solutions are efficient, robust and practical by experiments on
    synthetic and real data.},
}